module module high

`IndisputableMonolith.CrossDomain.CubeFaceUniversality`

The CubeFaceUniversality module defines a predicate for types with exactly six elements and verifies this property for quarks, leptons, cortical layers, Braak stages, and robotic degrees of freedom. Researchers in Recognition Science cite these instances to show the six-face cube geometry appears across particle physics and neuroscience. The module proceeds by direct definition of the predicate followed by explicit cardinality checks for each listed type.

claimA type $T$ satisfies HasCubeFaceCount if and only if $|T|=6$.

background

Recognition Science obtains three spatial dimensions from the forcing chain, which produces a cubic geometry whose six faces supply the target count. This module introduces the cross-domain predicate HasCubeFaceCount that captures any type whose cardinality equals six. It then instantiates the predicate for the concrete types Quark, Lepton, CorticalLayer, BraakStage, and RoboticDOF.

proof idea

This is a definition module, no proofs.

why it matters in Recognition Science

The module supplies concrete instances that feed the cube_face_identity result and the broader claim that D=3 forces six-element structures in multiple domains. It links the geometric output of the forcing chain to observable counts in fundamental particles and biological staging systems.

scope and limits

Does not derive the number six from the forcing chain inside this module.
Does not claim every domain obeys the six-element rule.
Does not connect the count to mass formulas or coupling constants.
Does not supply a general existence theorem for six-element sets.

declarations in this module (20)

def HasCubeFaceCount L29
inductive Quark L31
inductive Lepton L35
inductive CorticalLayer L39
inductive BraakStage L43
inductive RoboticDOF L47
theorem quark_has_6 L51
theorem lepton_has_6 L53
theorem cortical_has_6 L55
theorem braak_has_6 L57
theorem robotic_has_6 L59
theorem cube_face_identity L63
theorem q3_euler L66
theorem cube_face_equicardinal L69
theorem quark_lepton_sum L76
theorem fermion_antifermion_total L81
theorem cube_face_cubed L86
theorem six_cubed L94
structure CubeFaceUniversalityCert L96
def cubeFaceUniversalityCert L107